96 Normat 53:2, 96 (2005)

Summary in English

Erik M. Alfsen, Karl Egil Aubert

1924–1990 (Norwegian).

A brief biography of the Norwegian al-

gebraist Karl Egil Aubert.

Uﬀe Thomas Jankvist and Nesli-

han Saßlanmak, What did they seek

and what did they ﬁnd? Combinatoric

solutions for algebraic equations – from

Cardano to Cauchy – Part 1 (Danish).

A history of algebraic equation solving

before Gauss, Abel and Galois, more

speciﬁcally in the period from 1545

to 1815. In this ﬁrst part of the ar-

ticle the authors present the methods

of Cardano, Viète, Tschirnhaus, Waring

and Vandermonde, but also discuss con-

tributions from Ferrari, Girard, Euler

and Bézout. The article foc uses on the

use of combinatorics, permutations and

invariance considerations in algebraic

equation s olving. Some of the points

made in Part 1 concern the inﬂuence of

alchymistic thoughts in these methods.

Also the authors argue that the period

from 1546 to 1770 is not as ‘blunt’ as it

might seem at ﬁrst glance.

Ståle Gundersen, Does it follow from

Gödel’s incompleteness theorems that

we are not machines? (Norwegian).

The Austrian logician Kurt Gödel

proved the two incompleteness theo-

rems in 1931. The ﬁrst of these states

that within each mathematical formal

system there exists a true sentence (the

Gödel sentence) that cannot be proven

within the formal system. The second

states that the consistency of a formal

system cannot be proven by the system

itself. Since computers are machines

which can instantiate formal systems,

the philosopher J. R. Lucas and the

physicist and mathematician R. Penrose

have argued that Gödel’s two incom-

pleteness theorems imply that human

beings cannot be machines (computers).

According to their argument, we are not

machines be cause we know we can be

consistent, but unlike the machines we

can also prove that the Gödel sentence

is true. The author presents the Lucas/

Penrose argument and rejec ts it as in-

valid.

Johan Häggström, The concept of

function in historical light (Swedish).

In spite of being one of the most impor-

tant mathematical concepts, the con-

cept of function can be, and has been,

described and deﬁned in many ways.

The article exposes the diversity by

showing examples from textbooks and

by a brief journey through the history

of function. Three aspects of the devel-

opment are highlighted.